Guided only by radar, Phalanx and the land-based C-RAM have not only detected but intercepted many artillery and mortar shells. This requires a 3D spatial solution within a few inches: C-RAM - Wikipedia
The Israeli Iron Dome radar system has intercepted many mortar shells and Qassam rockets which are about man-sized. These are not only detected but the missile is radar-guided to an intercept in 3D space. Admittedly there is a handoff in the terminal phase to on-board radar, but Patriot PAC-2 has intercepted small artillary rockets using only ground-based radar: https://youtu.be/TwyImK6KCTc?t=25
So it depends on the radar system and what it’s designed to achieve. While NOAA’s WSR-88D weather radar can detect swarms of bugs and birds, as already stated it cannot detect an individual bird, at least with the current processing system.
The Navy’s SPY-1A phased array Aegis radar system has roughly the same angular resolution as the WSR-88D but obviously has processing designed to detect smaller objects, probably from doppler discrimination. Your point about a static object may be valid – if superman was hovering, not moving in three dimensions relative to the radar, maybe he couldn’t be detected by something like SPY-1A.
My point was clocking a moving object is not sufficient and exclusionary evidence of radar, and neither does arriving at the rate of change of motion of the object, which is one step removed from OP.
You can use Doppler acoustics for the same job in many circumstances.
My car can detect people walking toward it from the rear quarters. They call it "rear cross-traffic alert. The documentation says it’s “radar”, but who knows if they’re using the correct term? All I can tell for sure is that the people who set off the alert are not within the viewing field of the backup cam.
My escape has infra red beams that project out to the rear in an arc, anyone or thing that breaks the beam sounds the audible alert. For your car to actually have some sort of radar, I would expect that your documentation should show some sort of FCC side doc’s on how much milimeter wave radar that its putting out, and any kind of radiation warnings.
They’re both parts of the EM spectrum, but radar specifically refers to devices using one particular portion of the spectrum. An IR-based system would probably be lidar.
